Divisibility by 6

How can we tell whether an integer is divisible by 6? A number is divisible by 6 if it is both divisible by 2 and divisible by 3. As a reminder:

• An integer is divisible by 2 if its last digit is even, that is, one of the digits 0, 2, 4, 6 or 8.
• An integer is divisible by 3 if the sum of its digits is divisible by 3.

Examples:

• The number 15 is divisible by 3, but not by 2, so it is not divisible by 6 either.
• The number 22 is divisible by 2, but not by 3, so it cannot be divisible by 6 either.
• The number 42 is divisible by 2, because it ends in the digit 2, and it is divisible by 3, because the sum of its digits is 6. So it is divisible by 6 too.